Question

(sin Θ − cos Θ)^2 + (sin Θ + cos Θ)^2

Answer 1

Okay so I know that it will will be (sin Θ − cos Θ)^2 + 1 but i dont know what to do after

Answer 2

the four answers are
−sin2 Θ

−cos2 Θ

0

2

Answer 3

\(\normalsize\color{blue}{ \rm sin Θ + cos Θ=1 }\) and
\(\normalsize\color{blue}{ \rm (sin Θ - cos Θ)^2=sin^2Θ-2sinΘcosΘ+cosΘ= }\)
\(\normalsize\color{blue}{ \rm 1-2sinΘcosΘ=1-sin(2Θ) }\)

thus you get,
\(\normalsize\color{blue}{ \rm 1-sin(2Θ)+1 }\)
\(\normalsize\color{blue}{ \rm 2-sin(2Θ) }\)

Answer 4

for the 2nd blue line it should be \(\normalsize\color{blue}{ \rm sin^2Θ-2sinΘcosΘ+cos^2(Θ) }\) at the end of the line.

Answer 5

so what is the final answer?

Answer 6

2-sin(2 Θ) is not in the answers

Answer 7

Here is the solution :

\[\large{(\sin{\theta} - \cos{\theta})^2 + (\sin{\theta} + \cos{\theta})^2}\]

\[\large{= \sin^2{\theta} + \cos^2{\theta} - 2\sin{\theta}\cos{\theta} + \sin^2{\theta} + \cos^2{\theta} + 2\sin{\theta}\cos{\theta}}\]

Now, solve it after this. Remember that \(\large{\sin^2{\theta} + \cos^2{\theta} = 1}\)

Answer 8

I don't know how to solve it

Answer 9

can you please help me

Answer 10

would the answer be 1?

Answer 11

i mean 2

Answer 12

Yeah you are perfectly right.

Answer 13

thank youuuu

Answer 14

:) np

Answer 15

\[
(\sin (\theta )-\cos (\theta ))^2+(\sin (\theta )+\cos (\theta ))^2=\\\sin
^2(\theta )+\sin ^2(\theta )+\cos ^2(\theta )+\cos ^2(\theta )+2 \sin
(\theta ) \cos (\theta )-2 \sin (\theta ) \cos (\theta )=\\2 \sin
^2(\theta )+2 \cos ^2(\theta )=2

\]